414 BELL SYSTEM TECHNICAL JOURNAL 



balanced two-wire lines, and to the apparatus associated with these 

 two line types. 



II. Concentric-Tube Lines 



A shielded line comprising an inner tubular conductor and an outer 

 concentric shield is the form most commonly employed in radio prac- 

 tice. Owing to the circular symmetry of the line the case is capable of 

 rather exact mathematical analysis. At radio frequencies the results 

 are surprisingly simple. This simplicity is very evident for the two 

 important parameters of a transmission line, the propagation constant 

 P and the characteristic impedance Zq. 



The propagation constant of a line is defined by: 



P = Vi?+>L-VG + jcoC, (1) 



in which 



{R + jcoL) is the complex impedance and 



(G + jcoC) is the complex admittance, both per unit length. It is 

 well known that the propagation constant is a complex number and 

 that at radio frequencies (1) reduces to: ^ 



P = « + 7/3 = 22^- + ^- + — , (la) 



in which R is the resistance and G is the leakage conductance, both per 

 unit length and at the wave-length X. 



The characteristic impedance Zo is defined by the ratio: 



The characteristic impedance also is a complex quantity, but at radio 

 frequencies it is for most practical purposes the real quantity: 



^0 = ^ • (2a) 



In the case of concentric-tube lines the expression for the capacity C 

 per unit length is the familiar relation : 



1 

 C ^e.s.u., 



2 log.- 



in which a is the outer radius of the inner conductor and b is the inner 

 radius of the outer conductor. The inductance L per unit length may 

 ^ J. A. Fleming, "The Propagation of Electric Currents." 



